Myerson treated various situations of cooperation in the field of cooperative games and proposed the communication structure. In this paper, we define and characterize an allocation rule in terms of the position value, called an average spanning tree solution, for communication situations by introducing a concept of cooperation relationship which says that two players are deemed to possess this...

Let R be a fnite commutative ring and N(R) be the set of non unit elements of R. The non unit graph of R, denoted by Gamma(R), is the graph obtained by setting all the elements of N(R) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x - yin N(R). In this paper, the basic properties of Gamma(R) are investigated and some characterization results regarding co...

Two-strategy evolutionary games on graphs have been extensively studied in the literature. A variety of graph structures, degrees of graph dynamics, and behaviours of replicators have been explored. These models have primarily been studied in the framework of facilitation of cooperation, and much excellent work has shed light on this field of study. However, there has been little attention to t...

Let N = {1, . . . , n} be a finite set. Let E be a collection of ordered or unordered pairs of distinct 1 elements from N . A graph G is defined by (N,E). The elements of N are called vertices of graph G. The elements of E are called edges of graph G. If E consists of ordered pairs of vertices, then the graph is called a directed graph (digraph). When we say graph, we refer to undirected graph,...